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Scalar Products of Certain Hecke L-Series and Moments of Weighted Norm-Counting Functions

Published online by Cambridge University Press:  20 November 2018

R. W. K. Odoni
R. W. K. Odoni*
Affiliation:
Department of Mathematics, University of ExeterExeter Ex4 4qe, England
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Abstract

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We consider Dirichlet series R(s), constructed by taking scalar products of Hecke L-series with ray-class characters. Using a theorem of G. W. Mackey on tensor products of representations of finite groups we show that R(s) has a meromorphic continuation into Re(s) > 1/2 (obtained by more sophisticated methods in [l]-[5]); we then obtain estimates for the growth of R(s) on vertical lines. Via the Mellin transformation we deduce asymptotics for various weighted moment sums involving ideals of given ray-class and norm, in one or several fields simultaneously.

Keywords

12A7012A55
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 28 , Issue 3 , 01 September 1985 , pp. 272 - 279
Copyright
Copyright © Canadian Mathematical Society 1985

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